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Structure of Water and Hydrophobic Bonding in Proteins. II. Model for the Thermodynamic Properties of Aqueous Solutions of Hydrocarbons
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21.Throughout this paper, the standard states are taken as mole fraction unity () in the liquid and the solution, and the pressure 1 atm in the gaseous state.
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24.The interactions vary with the different polar character of the solvents. In particular, interactions between aliphatic and aromatic hydrocarbons in binary mixtures differ from those between aliphatics or aromatics themselves, as indicated by lowered solubilities for aliphatic‐aromatic systems,25 and by positive deviations from ideality in benzene‐cyclohexane mixtures.26
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39.In our preliminary communication,† an energy level diagram based on more crude considerations was presented. Since then, the theory has been refined, resulting in some changes in the description of the interactions. The correct energy diagram (Fig. 2) differs in part from the earlier one and supersedes it.
40.cf. reports on “hydrogen‐bond formation” between OH‐groups and π electrons.41,42
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44.In the case of the side chains of the amino acids of proteins, to be discussed in Part III,3 this assumption will no longer be valid. The concentration of side chains can be relatively large over limited regions in space. The effect of this increased concentration is a factor that has to be considered explicitly in the discussion of the hydrophobic bond.
45.The consideration of the interaction energies presented here also explains why solid gas hydrates can be stable. They, too, are stabilized by the energy gain resulting from the increase in the effective coordination number of the hydrogen‐bonded water molecules forming the walls of the cages. In the crystal, the solute molecules in neighboring cages act cooperatively in stabilizing the structure, as a given water molecule can interact with more than one solute molecule.
46.cf. footnote 45. In the gas hydrate crystals, most of the cavities must usually be occupied by gas molecules for the hydrate to exist.
47.Frank and Wen43 state that “ice‐likeness” increases more or less proportionately to the size of the nonpolar region of a solute molecule and hence they reject the hypothesis of cage formation27 as a source of “ice‐likeness.” Our concept of partial cage formation is consistent with their proposal as it can allow for a practically continuous change in properties with size.
48.Throughout this paper, the superscript c designates the first layer around the solute, to distinguish the parameters describing it from the parameters used for pure water.
49.A molecule with three hydrogen bonds in the first layer next to the solute but with no fourth bond would experience an increase in coordination number and hence a lowering of its energy level, similar to the tetra‐bonded molecule. However, such a structure could only exist if the cage were to form an entity of its own, i.e., a monomolecular layer of hydrogen‐bonded molecules next to the solute. This condition is inconsistent with the basic premises of the model for water (cf. Part I), and therefore the existence of such structures can be precluded.
50.We acknowledge here the opportunity for the use of the facilities of the Cornell Computing Center.
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58.We follow the usual convention of considering attractive intermolecular energies as negative. Thus and appearing in the discussion are all quantities less than zero.
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65.Complete tables of the computed thermodynamic parameters for all hydrocarbon solutions considered, as well as the computing programs employed in their calculation, are published elsewhere.66
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71.The values given69 for methane and ethane in hexane solution are apparent molal volumes, not partial molal volumes. The two are not equal in general but have been found so, experimentally,69 in this case.
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